## Monday, 30 May 2016

### Exploring Student Wonderings: Prime / Composite Numbers

What can we do with student wonderings?

We know that they are the driving force of authentic learning and are pivotal to inquiry-based learning.

In maths we sometimes tap into these as a whole class to investigate and share findings, sometimes groups or individuals explore and share.

For our recent enquiry into prime / composite numbers, I experimented with a different strategy. I wrote some of our class wonderings on paper and we used these to think about for our home learning that week.  Some of the wonderings we had already explored in class and so they could be used to consolidate / reinforce student understandings. Others, we hadn't tapped into directly so I thought it could be interesting to see how this might work.

Student sample:

During our enquiry, one student had an interesting wondering:

Could a connection exist between prime / composite numbers and primary /secondary colours?

This morning when we shared our theories from our home learning, we focused more on this wondering because it had created a lot of creative thinking.

With our partners, we shared and tried to combine our connections and then experimented with ways we could visually show our thoughts.

We used this in a whole class circle share and gave feedback to each other of not only the connections made but also the effectiveness of their visual communication skills.

Some samples:

When we give children opportunities to think creatively in maths, deeper conceptual understandings are certainly formed.

Some of our ideas:

° Because red is the first colour in the rainbow, it is like 1- special.

° Just like primary colours make all the secondary and tertiary colours, the factors of prime numbers make all the composite numbers.

° Prime numbers are like primary colours; if you mix them up, you get secondary (composite) colours.

° If prime numbers don't exist, we can't make our base 10 number system. Its the same with primary colours- without them we can't make all the other colours.

° Prime numbers are the 'building blocks' of all numbers and primary colours are the 'building colours' of all colours.

°

Asking my class what they thought of having some of our wonderings for home learning, they thought:

° It is helpful to have as much time as we need to think about them.

° I asked my parents their point of view to see if it matched mine; I thought that was interesting.

° For one of our wonderings, I didn't know. I couldn't think of a theory, but I was really curious so I searched the internet and learnt that way.

° I like that since we are creating theories, then there isn't any pressure to be right or wrong.

We all agreed that we should do this more often.